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The pre-WDVV ring of physics and its topology

Margaret A. Readdy
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Abstract

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex $Δ_n$ is homotopy equivalent to a wedge of $(n-2)!$ spheres of dimension $n-4$. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex and the Hilbert series of the associated pre-WDVV ring.

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Margaret A. Readdy. 2005-11-16. The pre-WDVV ring of physics and its topology. https://doi.org/10.1007/s11139-005-4850-1

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